Gaussianization is a simple generative model that can be trained without backpropagation. It has shown compelling performance on low dimensional data. As the dimension increases, however, it has been observed that the convergence speed slows down. We show analytically that the number of required layers scales linearly with the dimension for Gaussian input. We argue that this is because the model is unable to capture dependencies between dimensions. Empirically, we find the same linear increase in cost for arbitrary input $p(x)$, but observe favorable scaling for some distributions. We explore potential speed-ups and formulate challenges for further research.

翻译：高斯化是一种无需反向传播即可训练的简单生成模型，在低维数据上展现了令人瞩目的性能。然而，随着维度的增加，其收敛速度会减缓。我们从解析角度证明，对于高斯输入，所需层数与维度呈线性增长。我们认为这是由于该模型无法捕捉维度间的依赖关系所致。实验验证发现，对于任意输入$p(x)$，计算成本均呈相同线性增长，但部分分布展现出更优的缩放特性。我们探讨了潜在加速策略，并提出了未来研究方向的关键挑战。